Catching all geodesics of a manifold with moving balls and application to controllability of the wave equation

Autor: Cyril Letrouit

Publikováno v: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2023, XXIV, pp.15. ⟨10.2422/2036-2145.202010_004⟩
Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore In press

We address the problem of catching all speed $1$ geodesics of a Riemannian manifold with a moving ball: given a compact Riemannian manifold $(M,g)$ and small parameters $\varepsilon>0$ and $v>0$, is it possible to find $T>0$ and an absolutely continu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fa2773dd019c4d937607f7071b4fe109
https://hal.science/hal-02102135

Propagation of well-prepared states along Martinet singular geodesics

Autor: Yves Colin de Verdière, Cyril Letrouit

Publikováno v: Journal of Spectral Theory
Journal of Spectral Theory, In press, ⟨10.48550/arXiv.2105.03305⟩
Journal of Spectral Theory, European Mathematical Society, In press

We prove that for the Martinet wave equation with "flat" metric, which a subelliptic wave equation, singularities can propagate at any speed between 0 and 1 along any singular geodesic. This is in strong contrast with the usual propagation of singula

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::51117b96617e3364fa2c8f12415df08a
https://hal.archives-ouvertes.fr/hal-03220110/document

Observability and Controllability for the Schrödinger Equation on Quotients of Groups of Heisenberg Type

Autor: Clotilde Fermanian Kammerer, Cyril Letrouit

Publikováno v: Journal de l'École polytechnique — Mathématiques
Journal de l'École polytechnique — Mathématiques, École polytechnique, 2021
Journal de l'École polytechnique — Mathématiques, 2021, ⟨10.48550/arXiv.2009.13877⟩
Journal de l'École polytechnique — Mathématiques, École polytechnique, 2021, ⟨10.48550/arXiv.2009.13877⟩

We give necessary and sufficient conditions for the controllability of a Schrödinger equation involving a subelliptic operator on a compact manifold. This subelliptic operator is the sub-Laplacian of the manifold that is obtained by taking the quoti

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b5ba985b4fcdcdd3796c8feed15991ad
https://hal.archives-ouvertes.fr/hal-02951662/file/Observabilite-FKL-vf.pdf